What is the most impactful way of introducing Laplace transforms?

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Discussion Overview

The discussion focuses on how to effectively introduce Laplace transforms to engineering students, exploring various applications and contexts where these transforms are relevant. The scope includes theoretical insights, practical applications, and considerations for different engineering disciplines.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants emphasize that Laplace transforms are essential for linear systems analysis, particularly in fields like analog circuit design, filter design, and control systems.
  • One participant notes that Laplace transforms are crucial for transient analysis in linear systems, highlighting the importance of poles and zeros in the Laplace transfer function.
  • Another participant mentions the utility of Laplace transforms in solving nonhomogeneous ordinary differential equations (ODEs), particularly in electrical circuits and mechanical systems involving springs and damping.
  • There is a suggestion to introduce the z-transform as a related concept for discrete time systems, indicating that Laplace transforms represent a broader analytical framework.
  • A participant questions the specific engineering background of the students, suggesting that applications may vary significantly between electrical engineers and mechanical engineers.
  • One participant points out that aerospace engineers utilize Laplace transforms in flight control design and stability analysis.

Areas of Agreement / Disagreement

Participants generally agree on the importance of Laplace transforms in various engineering applications, but there is no consensus on the best approach to introduce the topic, particularly regarding the specific engineering disciplines involved.

Contextual Notes

The discussion highlights the need for context-specific examples when introducing Laplace transforms, as different engineering fields may require different applications and motivations.

Who May Find This Useful

This discussion may be useful for educators in engineering disciplines, particularly those teaching courses related to circuit analysis, control systems, and differential equations.

matqkks
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I am trying to find a motivating way to introduce Laplace transforms to engineering students. Looking for concrete examples where they might need Laplace transforms.
 
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It is THE main tool for linear systems analysis (often non-linear systems too). Analog circuit design, filter design, control systems, state space analysis, etc. We do nearly everything in the s domain. Also nearly the only good way to do transient analysis in linear systems. It's all about the poles and zeros in the Laplace transfer function.

In my world the impedance of an inductor isn't L, it's sL. Linear circuit analysis starts and often ends in the s domain, you transform back to time only when you have to.
 
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Laplace transforms are also useful in solving nonhomogeneous ODES such as those that describe LRC electrical circuits with an AC driving voltage. These transforms are also useful in solving ODEs that describe mechanical systems that involve a spring, mass, and damping device, and that have a driving force acting on them.
 
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I might also mention, but not teach, the z-transform. It's essentially the Laplace equivalent for discrete time systems; digital controls and such. Just to show that it's not a one-off tool, it's a fundamental way of thinking about analysis.
 
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matqkks said:
motivating way to introduce Laplace transforms to engineering students.
What kind of Engineering students? Are they EEs? If so, as @DaveE says Laplace Transforms are used in most of circuit analysis. If they are mostly MEs or some other type of engineering, we probably need to think more about good applications that are used in their specialty.
 
matqkks said:
I am trying to find a motivating way to introduce Laplace transforms to engineering students. Looking for concrete examples where they might need Laplace transforms.
linear ode with delay for example
 
Aero engineers in flight control design or stability and control use it heavily.
 
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